Black areas in glossy surface
OK I looked at your blend, and it was nothing more then the reflection of the shadow from the other objects. 

First off I whent into edit mode, selected everything with A A, then on the tool shelf under the Shading/UV tab pressed the Recalculate button. Half of the normals were backwards. 

The main thing I did was add a Diffuse node to your material, connected to a Mix Shader. The diffuse node gives the material a base color, regardless of reflections. Then mixed with the glossy node will add some reflections back to the material.

You really need something for the glossy shader to reflect off of, if you are going to get any reflections. A HDR is commonly used.

Modified blend